They don't count the NZ-Singapore switches in '84 w/ Harley Race. They were done without the authorization of the NWA at the time and were thus ignored in all the old territories, even though the "modern" NWA retroactively decided to recognize them in the early 90s. The strange part though is that although they don't include it in Flair's # of titles, they do and/or have for Race and have referred to him as an 8 time World Champion.

Flair's victory over Sting in 1991 for the NWA/WCW World title is considered a single championship win, even though he essentially won two different titles. World Championship Wrestling treated the WCW title as an extension of the NWA title and made no distinction between the two until the NWA title was revived as a separate championship in 1992. They also don't count the NWA only switch with Tatsumi Fujinami that occurred in Japan which likewise wasn't recognized by WCW at the time it happend.

The "World Title" that Flair lost to Rick Rude in 1993 was treated by World Championship Wrestling as an extension of his NWA title reign/win over Barry Windham, even though the NWA (after parting ways with WCW) had officially stripped him of the championship before the match took place. After legal action by the Alliance, WCW removed championship recognition from what then became known as just "The Gold Belt" before reinstating it as a championship in the form of the "WCW International" World title.

They also don't count his victory over Ricky Steamboat in 1994 for the held-up WCW title as a new reign (WCW did initially before rescinding) and the unification win over Sting the same year is also not recognized as an additional title.

It should be noted that when Flair returned to WCW from the WWF in 1993, he was constantly called a 9 time World Champion, an obvious reference to the two additonal titles he had won in the WWF. I believe they even explicitly mentioned it. However, in later WCW publications and/or arena programs that listed his title history, his two WWF reigns were ignored and in turn substituted with the previously unrecognized NWA switch with Harley Race from 1984 as well as the switch with Tatsumi Fujinami from 1991. I also seem to remember them being included in the "NWA/WCW World title" history that appeared on the WCW website which, for some reason, started with the Giant Baba in 1980 (and which also completely ignored the fact that the NWA title existed in World Championship Wrestling as a separate championship from the WCW title in 1992-93). But as mentioned, WWE does not recognize those as an "official" part of *their* Flair title history.